The radial motion of photons in Kerr metric

Radial motion of photons through the Kerr spacetime is analyzed for both the black holes and the naked singularities. The regions allowed for radial motion are determined in terms of constants of motion of photons. Figures are drawn to exhibit the qualitatively different behaviour of these regions. It is shown that the qualitative behaviour is of the same character for all black holes, while it depends on the parameter α=a/M of the Kerr naked singularities. In the case of naked singularities a large vortex could be formed by photons in stable spherical orbits concentrated around the shell of zero-energy photons, located at the surface r=M. In the field of a Kerr black hole these spherical orbits may exist under the inner horizon only, and for zero-energy photons they cannot exist at all. (author)